Communicating Mathematics

Communicating well is a critical component of being a successful research mathematician.

Papers that are easy to read find more readers, which means more citations, more recognition and more potential collaborators for the authors. Of course, well-written papers sail much more quickly and easily through the peer review process.

Beyond research papers, mathematicians write grant proposals.  Some are directed at experts in their field, but many are written for a general mathematical or scientific audience, or sometimes deans or politicians more broadly.  Well-written proposals,  accurately aimed at the correct target audience, are much more likely to get funded.

Talks that are accessible to a wide audience expand the network of mathematicians who appreciate your work. Talks that folks in your field can understand nurture collaborations.

Likewise, every talk is a job talk. Prepare, know your audience, teach something. You never know who is listening who may later mention your name to a department looking to hire in your field.

Math professors, just like professionals in any sector, write annual reports for each of their funded projects, whether to the NSF, private foundations, or their own University. They also write annual progress reports to their chair or dean; these play a critical role in determining their salary for the following year.

A typical math professor writes tens of letters of recommendation each year: these letters are probably the most important part of the students’ applications.

Mathematicians who can write and speak well have a tremendous advantage in getting publications, speaking invitations, citations, grants, fellowships, salary raises and well-placed students. Investing in becoming a better writer and speaker is an investment in  your career success.

Advice on Reading and Listening to Mathematics

UM Resources to improve your Writing

Take advantage of the resources offered by Michigan’s Sweetland Center for Writing. This is a great place to get advice on improving your writing, and sometimes even get paid to get that help! For example, through Sweetland you can:

  • Meet with a writing expert to go over a grant proposal, research paper, dissertation passage, or any writing for a class. They’re not mathematicians, but YES they can help with math writing (this has been tested)
  • Take a class that helps you write a research paper or your dissertation
  • Join a dissertation writing group. You can even get paid to be a group leader.
  • Consider applying for the Sweetland Writing Institute, a summer fellowship for students in the final stages of  dissertation writing. This can supply a stipend in the summer without teaching, so that you can complete your degree.
  • Consider applying for to be a Sweetland Fellow; this will give you an opportunity to teach writing about math as a GSI in the English Department. Rachel Webb recently did this.

Advice on Writing from around the web

Advice on Speaking and Listening to Mathematics from around the web

Advice on preparing job documents

Advice on preparing job documents from the Mathematics Students Resource

Advice on writing grant applications

Advice on writing grant applications from the Mathematics Students Resource

Become Familiar with the Literature
  • Search MSC (Mathematics Subject Classification) codes. An MSC code (eg 14N35) identifies a narrow subfield of math.
    • First find codes you are interested in. You can browse the complete index of MSC codes. Or, search MathSciNet for a particular paper that you are interested in and see what codes it is assigned (You can also use ZbMath  though the codes will be different.)
    • On MathSciNet, you can click directly on the code to see a list of all papers with this classification. Or, find multiple codes that you are interested in and search these from MathSciNet’s homepage (under “Search Terms” select “MSC Primary/Secondary”).
  • Browse the arxiv.  This is where mathematicians post their preprints. You can subscribe here  to get daily emails listing the author/title/abstract of new papers in whatever subjects interest you.
  • Search forwards/backwards citations with google scholar or MathSciNet
  • Talk to people

Read high quality mathematics

Peer review

Get a group of friends to discuss your current writing projects or upcoming presentations. This is one of the best ways to improve your mathematical communication. (Here’s why.) (And more reasons from the MAA.)

Advice on Preparing Conference Posters

Mathematicians who have made careers from writing

Evelyn Lamb who has a mathematics blog for Scientific American blog

Erica Klarreich, a free-lance science writer with extensive contributions, for example, to Quanta Magazine.

Mathematics in the popular culture

Mathematics in the popular culture:

Quanta Magazine.

Scientific American